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%I #47 Aug 21 2023 10:27:56
%S 1,1,7,8,5,1,1,3,0,1,9,7,7,5,7,9,2,0,7,3,3,4,7,4,0,6,0,3,5,0,8,0,8,1,
%T 7,3,2,1,4,1,3,9,3,2,2,9,4,8,0,7,9,0,0,6,0,9,8,0,5,6,6,4,4,8,3,2,5,6,
%U 1,0,3,9,8,7,1,8,4,2,2,5,3,2,3,7,5,3,2,2,9,4,5,2,7,3,0,3,4,6,4
%N Decimal expansion of 1/sqrt(72) = 1/(3*2^(3/2)) = sqrt(2)/12.
%C Volume of regular tetrahedron with unit edge. - _Stanislav Sykora_, May 31 2012
%C In the dragon curve fractal, (5/6)*sqrt(2) = 1.1785.... is the maximum distance of any point from curve start. Such a maximum must be to a vertex of the convex hull. Hull vertices are shown by Benedek and Panzone (theorem 3, page 85) and their P8 = 7/6 - (1/6)i at distance sqrt((7/6)^2 + (1/6)^2) is the maximum. - _Kevin Ryde_, Nov 22 2019
%H Ivan Panchenko, <a href="/A020829/b020829.txt">Table of n, a(n) for n = 0..1000</a>
%H Agnes I. Benedek and Rafael Panzone, <a href="https://inmabb.criba.edu.ar/revuma/pdf/v39n1y2/p076-089.pdf">On Some Notable Plane Sets, II: Dragons</a>, Revista de la Unión Matemática Argentina, volume 39, numbers 1-2, 1994, pages 76-90.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetrahedron">Tetrahedron</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>.
%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F Equals Integral_{x=0..Pi/4} sin(x)^2 * cos(x) dx. - _Amiram Eldar_, May 31 2021
%e 0.117851130197757920733474...
%t RealDigits[sqrt(2)/12, 10, 50][[1]] (* _G. C. Greubel_, Jul 06 2017 *)
%o (PARI) sqrt(2)/12 \\ _G. C. Greubel_, Jul 06 2017
%Y Cf. A131594 (regular octahedron volume), A102208 (regular icosahedron volume), A102769 (regular dodecahedron volume).
%K nonn,cons
%O 0,3
%A _N. J. A. Sloane_
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